{smcl} {* Help file update 2020-04-21,2010-05-20,2010-03-09, 2009-09-15}{...} {hline} help for {hi:sgini}{right:P. Van Kerm (April 2020, February 2010, September 2009)} {hline} {title:Title} {pstd}{hi:sgini} {hline 2} Generalized Gini and Concentration coefficients (with factor decomposition) {title:Syntax} {p 8 15 2} {cmd:sgini} {it:varlist} [{it:weight}] [{cmd:if} {it:exp}] [{cmd:in} {it:range}] [{cmd:,} {it:options}] {synoptset 22 tabbed} {synopthdr} {synoptline} {synopt :{opth p:arameters(numlist)}}specifies inequality aversion parameters{p_end} {synopt :{opt source:decomposition}}requests factor decomposition (decomposition by source){p_end} {synopt :{opt aggr:egate}} switches to computation of S-Gini welfare indices{p_end} {synopt :{opt wel:fare}} is synonymous to {opt aggr:egate}{p_end} {synopt :{opt abs:olute}}switches to computation of absolute S-Gini indices{p_end} {synopt :{opth s:ortvar(varname)}}sets ordering variable for Concentration coefficients{p_end} {synopt :{opth frac:rankvar(varname)}}passes a varname with existing fractional ranks{p_end} {synopt :{opth for:mat(%fmt)}}display format; default is {cmd:format(%5.4f)}{p_end} {synoptline} {p 4 8 2} {it:varlist} may contain time-series operators; see {help tsvarlist}. {p_end} {p 4 6 2}{cmd:bootstrap}, {cmd:jackknife}, {cmd:svy bootstrap}, and {cmd:svy jackknife} prefixes are allowed; see {help prefix}.{p_end} {p 4 6 2}{cmd:fweight}, {cmd:aweight} and {cmd:pweight} are allowed; see help {help weights:weights}. {p_end} {title:Description} {pstd} {hi:sgini} is a command for calculations of generalized Gini (a.k.a. S-Gini) and Concentration coefficients from unit-record data. {hi:sgini} computes relative (scale invariant) Gini indices of inequality by default but can be requested to produce absolute (translation invariant) indices or aggregate welfare S-Gini indices. The command can also optionally report decomposition by factor components (income sources). {p_end} {pstd} Multiple variables and multiple inequality aversion parameters can be passed to {hi:sgini}. Beware that if multiple variables are input, {hi:sgini} will discard observations with missing data on {it:any} of the input variables and compute all coefficients on the resulting sample. {p_end} {pstd} {cmd:sgini} does not provide sampling variance estimates (as an r-class command) but it is easily bootstrapped using a {cmd:bootstrap} or {svy bootstrap} prefix. See the user-written {help svylorenz}, {help lorenz} or {help inequaly} for estimation of Gini coefficients with (analytic) standard errors. {p_end} {pstd} An accompanying {browse "http://www.vankerm.net/stata/manuals/sgini.pdf":online manual} provides details on formulas, option descriptions and usage examples. {p_end} {title:Options} {phang} {opth p:arameters(numlist)} specifies inequality aversion parameters. Default is 2 leading to the standard Gini and Concentration coefficients. Multiple parameters can be requested. {p_end} {phang} {opth s:ortvar(varname)} sets ordering variable for Concentration coefficients. Default is to cumulate the variable(s) of interest against themselves, leading to Gini coefficients. {p_end} {phang} {opth frac:rankvar(varname)} passes the name of an existing variable containing fractional ranks based on which the Gini and Concentration coefficients can be computed. This is a rarely used and dangerous option, but it may provide considerable speed gains under certain circumstances. It is essential that the fractional rank variable be computed correctly (using e.g. {hi:fracrank}), and on the adequate (sub-)sample (think missing data, {hi:if} clauses, ordering). Use carefully! {p_end} {phang} {opt source:decomposition} requests factor decomposition of indices. It is relevant when more than one variable is passed in {it:varlist}. It requests that a variable be created by taking the row sum of all elements in {it:varlist}, computes the Gini (or Concentration) coefficient for this created variable, and estimates the contribution of each element of {it:varlist} to the latter by applying the 'natural' decomposition rule for Gini coefficients (see Lerman & Yitzhaki, 1985). {p_end} {phang} {opt aggr:egate} and {opt abs:olute} request, respectively, computation of aggregate S-Gini welfare measures or computation of absolute Gini and Concentration coefficients, instead of the relative inequality measures. They are mutually exclusive and incompatible with {opt sourcedecomposition}. {opt welf:are} is synonymous to {opt aggr:egate}. {p_end} {phang} {opth format(%fmt)} controls the display format; default is {cmd:format(%5.4f)}. {p_end} {title:Saved Results} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Matrices}{p_end} {synopt:{cmd:r(coeffs)}}estimated coefficients{p_end} {synopt:{cmd:r(parameters)}}parameters from {opth param(numlist)}{p_end} {synopt:{cmd:r(r)}}Gini correlations between source and total income (if {opt sourcedecomposition} requested){p_end} {synopt:{cmd:r(c)}}Concentration coefficients of each source (if {opt sourcedecomposition} requested){p_end} {synopt:{cmd:r(elasticity)}}elasticities between source and total Gini (if {opt sourcedecomposition} requested){p_end} {synopt:{cmd:r(s)}}factor shares (if {opt sourcedecomposition} requested){p_end} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Scalars}{p_end} {synopt:{cmd:r(N)}}number of observations{p_end} {synopt:{cmd:r(sum_w)}}sum of weights{p_end} {synopt:{cmd:r(coeff)}}estimated coefficient for first variable, first parameter{p_end} {synoptset 15 tabbed}{...} {p2col 5 15 19 2: Macros}{p_end} {synopt:{cmd:r(varlist)}}{it:varlist}{p_end} {synopt:{cmd:r(paramlist)}}list of parameters from {opth param(numlist)}{p_end} {synopt:{cmd:r(sortvar)}}{it:varname} if {opth sortvar(varname)} specified{p_end} {title:Example} {p 8 12 2}{inp:. use http://www.stata-press.com/data/r9/nlswork , clear } {p 8 12 2}{inp:. tsset idcode year } {p 8 12 2}{inp:. gen w = exp(ln_wage) } {p 8 12 2}{inp:. sgini w } {p 8 12 2}{inp:. sgini w , param(1.5(.5)5) absolute} {p 8 12 2}{inp:. sgini w L.w L2.w} {p 8 12 2}{inp:. sgini w L.w L2.w , sortvar(w)} {p 8 12 2}{inp:. sgini w L.w L2.w , source} {p 8 12 2}{inp:. bootstrap G=r(coeff) , reps(250) nodots : /// } {p 8 12 2}{inp: {space 5} sgini w if !mi(w) } {p 8 12 2}{inp:. jackknife G=r(coeff) rclass nodots : /// } {p 8 12 2}{inp: {space 5} sgini w if !mi(w) } {title:References} {p 4 8 2}Chotikapanich, D. C. & Griffiths, W. (2001), On calculation of the extended gini coefficient, Review of Income and Wealth, 47: 541{c -}547. {p 4 8 2}Lerman, R. I. & Yitzhaki, S. (1985), Income inequality effects by income source: A new approach and applications to the United States, Review of Economics and Statistics, 67(1): 151{c -}156. {p 4 8 2}Lopez-Feldman, A. (2006), Decomposing inequality and obtaining marginal effects, Stata Journal, 6(1): 106{c -}111. {title:Also see} {psee} Manual: {bf:[R] inequality} {psee} Online: {helpb descogini} (if installed), {helpb ineqdeco} (if installed), {helpb svylorenz} (if installed), {helpb inequal7} (if installed), among {stata "findit gini inequality":several others} {title:Author} {pstd}Philippe Van Kerm, Luxembourg Institute of Socio-Economic Research (LISER) and University of Luxembourg, philippe.vankerm@liser.lu {title:Acknowledgments} {pstd} This package was originally written for the MeDIM project ({it:Advances in the Measurement of Discrimination, Inequality and Mobility}) supported by the Luxembourg Fonds National de la Recherche (contract FNR/06/15/08) and by core funding for CEPS/INSTEAD by the Ministry of Culture, Higher Education and Research of Luxembourg. {* Version 4.0 2020-04-21} {* Version 3.0 2010-02-05} {* Version 2.0 2009-09-15}